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Optimal Growth with Polluting Waste and Recycling

Author

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  • Raouf Boucekkine

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

  • Fouad El Ouardighi

Abstract

We study an optimal AK-like model of capital accumulation and growth in the presence of a negative environmental externality in the tradition of Stokey (Int Econ Rev 39(1):1–31, 1998). Both production and consumption activities generate polluting waste. The economy exerts a recycling effort to reduce the stock of waste. Recycling also generates income, which is fully devoted to capital accumulation. The whole problem amounts to choosing the optimal control paths for consumption and recycling to maximize a social welfare function that notably includes the waste stock and disutility from the recycling effort. We provide a mathematical analysis of both the asymptotic behavior of the optimal trajectories and the shape of transition dynamics. Numerical exercises are performed to illustrate the analysis and to highlight some of the economic implications of the model. The results suggest that when recycling acts as an income generator, (1) a contraction of both the consumption and capital stock is observed in the long run after an expansion phase; (2) whether polluting waste is predominantly due to production or consumption, greater consumption and lower capital stock are obtained in the long run compared with the situation when recycling does not create additional income; (3) greater recycling effort and lower stock of waste are resulted in the long run.

Suggested Citation

  • Raouf Boucekkine & Fouad El Ouardighi, 2016. "Optimal Growth with Polluting Waste and Recycling," Post-Print hal-01447868, HAL.
    • Handle: RePEc:hal:journl:hal-01447868
    DOI: 10.1007/978-3-319-39120-5_7
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    References listed on IDEAS

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    1. Raouf Boucekkine & Aude Pommeret & Fabien Prieur, 2013. "Technological vs. Ecological Switch and the Environmental Kuznets Curve," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 95(2), pages 252-260.
    2. Fagnart, Jean-François & Germain, Marc, 2011. "Quantitative versus qualitative growth with recyclable resource," Ecological Economics, Elsevier, vol. 70(5), pages 929-941, March.
    3. De Beir, Jean & Fodha, Mouez & Magris, Francesco, 2010. "Life Cycle Of Products And Cycles," Macroeconomic Dynamics, Cambridge University Press, vol. 14(2), pages 212-230, April.
    4. Joseph E. Stiglitz, 1974. "Growth with Exhaustible Natural Resources: The Competitive Economy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 41(5), pages 139-152.
    5. Rafael Lusky, 1976. "A Model of Recycling and Pollution Control," Canadian Journal of Economics, Canadian Economics Association, vol. 9(1), pages 91-101, February.
    6. John Hartwick, 1977. "Intergenerational Equity and the Investment of Rents from Exhaustible Resources in a Two Sector Model," Working Paper 281, Economics Department, Queen's University.
    7. Hartwick, John M, 1977. "Intergenerational Equity and the Investing of Rents from Exhaustible Resources," American Economic Review, American Economic Association, vol. 67(5), pages 972-974, December.
    8. Raouf Boucekkine & Aude Pommeret & Fabien Prieur, 2013. "Technological vs. Ecological Switch and the Environmental Kuznets Curve," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 95(2), pages 252-260.
    9. Engelbert Dockner & Gustav Feichtinger, 1991. "On the optimality of limit cycles in dynamic economic systems," Journal of Economics, Springer, vol. 53(1), pages 31-50, February.
    10. Fouad Ouardighi & Hassan Benchekroun & Dieter Grass, 2014. "Controlling pollution and environmental absorption capacity," Annals of Operations Research, Springer, vol. 220(1), pages 111-133, September.
    11. Grant, Darren, 1999. "Recycling and market power: A more general model and re-evaluation of the evidence1," International Journal of Industrial Organization, Elsevier, vol. 17(1), pages 59-80, January.
    12. Joseph Stiglitz, 1974. "Growth with Exhaustible Natural Resources: Efficient and Optimal Growth Paths," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 41(5), pages 123-137.
    13. Stokey, Nancy L, 1998. "Are There Limits to Growth?," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(1), pages 1-31, February.
    14. Martin, Robert E, 1982. "Monopoly Power and the Recycling of Raw Materials," Journal of Industrial Economics, Wiley Blackwell, vol. 30(4), pages 405-419, June.
    15. David K. A. Barnes, 2002. "Invasions by marine life on plastic debris," Nature, Nature, vol. 416(6883), pages 808-809, April.
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    Cited by:

    1. Pommeret, Aude & Ricci, Francesco & Schubert, Katheline, 2022. "Critical raw materials for the energy transition," European Economic Review, Elsevier, vol. 141(C).
    2. Fabre, Adrien & Fodha, Mouez & Ricci, Francesco, 2020. "Mineral resources for renewable energy: Optimal timing of energy production," Resource and Energy Economics, Elsevier, vol. 59(C).
    3. El Ouardighi, Fouad & Kogan, Konstantin & Boucekkine, Raouf, 2017. "Optimal Recycling Under Heterogeneous Waste Sources and the Environmental Kuznets Curve," ESSEC Working Papers WP1711, ESSEC Research Center, ESSEC Business School.
    4. Lafforgue, Gilles & Rouge, Luc, 2019. "A dynamic model of recycling with endogenous technological breakthrough," Resource and Energy Economics, Elsevier, vol. 57(C), pages 101-118.
    5. Liange Zhao & Jianfeng Zou & Zhijian Zhang, 2020. "Does China’s Municipal Solid Waste Source Separation Program Work? Evidence from the Spatial-Two-Stage-Least Squares Models," Sustainability, MDPI, vol. 12(4), pages 1-20, February.

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    More about this item

    Keywords

    Calculus of Variations and Optimal Control; Optimization; Economic Theory/Quantitative Economics/Mathematical Methods; Operation Research/Decision Theory; Operations Management;
    All these keywords.

    JEL classification:

    • Q57 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Ecological Economics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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